vector w has magnitude 25.0 and direction angle 41.7 degrees. Calculate the horizontal and vertical components of w
1 answer:
Consider the attached picture. It represents a vector, centered in the origin with angle 41.7 degrees, and a circumference with radius 25, centered in the origin.
As you can see, the horizontal and vertical components of the vector correspond to the lengths of segments OD and OC, respectively.
You might recognize this scenario from you trigonometry class: if the circle had radius 1, we would have
Since the circle has radius 25, we have to scale those coordinates:
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Given:
The system of equations:
To find:
The number that can be multiplied by the second equation to eliminate the x-variable when the equations are added together.
Solution:
We have,
...(i)
...(ii)
The coefficient of x in (i) and (ii) are 1 and respectively.
To eliminate the variable x by adding the equations, we need the coefficients of x as the additive inverse of each other, i.e, a and -a So, a+(-a)=0.
It means, we have to convert into -1. It is possible if we multiply the equation (ii) by -5.
On multiplying equation (ii) by -5, we get
...(iii)
On adding (i) and (iii), we get
Here, x is eliminated.
Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.